Multiplex Network Inference With Sparse Tensor Decomposition for Functional Connectivity

Abstract

Functional connectivity (FC) is a graphlike data structure commonly used by neuroscientists to study the dynamic behaviour of brain activity. However, these analyses rapidly become complex and timeconsuming, since the number of connectivity components to be studied is quadratic with the number of electrodes. In this work, we address the problem of clustering FC into relevant ensembles of simultaneously activated components, yielding a multiplex network that reveals characteristic patterns of the epileptic seizures of a given patient. While k−means is certainly the most popular method for data clustering, it is known to perform poorly on large dimensional data sets, and to be highly sensitive to noise. To overcome the socalled curse of dimensionality, we propose a new tensor decomposition to reduce the size of the data set formed by FC time-series recorded for several seizures, prior to apply k-means. We propose an adapted procedure to infer a multiplex network from several FC time series, and we emphasise one particular variant that imposes sparsity constraint. Then, we conduct a real case study, applying the proposed sparse tensor decomposition to iEEG data to infer a multiplex network corresponding to the different stages of an epileptic seizure.

Semi-automatic Extraction of Functional Dynamic Networks Describing Patient's Epileptic Seizures

“…Moreover, contrary to our study, the decomposition from (44) does not integrate the different seizures of the same patient to obtain more reproducible FC subgraphs. Tools to decompose several modalities, like tensor decomposition (46)(47)(48), were already applied in neuroscience (41,49,50) and recently in the context of epilepsy (26). In (26), we proposed a specific tensor decomposition with relevant constraints to encourage the inference of interpretable clusters of FC common to several seizures of the same patient.…”

“…We expect each subgraph to comprise several brain nodes with high connectivity values. The paper is organized as follows: We extend our previous work (26) to seizures with different durations, we call this method the Brain-wide Timevarying Network Decomposition (BTND). On the application side, we validate the clinical use of the method on a larger clinical dataset.…”

Dynamic Community Detection for Brain Functional Networks During Music Listening With Block Component Analysis

“…Although dynamic community detection technique [30] has recently emerged as a powerful tool for tracking the topological reconfiguration of brain networks [18], [31], [32], [33], it is still not straightforward for module detection for time-varying networks within or across multiple subjects. We thus consider the tensor decomposition (or tensor component analysis) based methods for such dynamic community detection [18], [31], [34], [35], [36], [37] since the tensor decomposition enables multi-timescale dimensionality reduction both within and across temporal evolution for multiple subjects in a purely data-driven method. Tensor decomposition has recently been regarded as an extension of PCA for dynamic brain network analysis across subjects, where time-frequency vectorized adjacency matrices were formed into a tensor and decomposed into components characterizing brain network patterns with spectral-temporal features [9], [38], [39], [40] or temporal features [41], [42].…”